Finite Group DatabasebetaFinite Group Databasebeta| order | 8804 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D31×D71 |
| unambiguous semidirect product | (D31×C71)⋊C2 |
| unambiguous semidirect product | (C31×D71)⋊C2 |
| unambiguous semidirect product | D2201⋊C2 |
| Fitting, socle, derived, Hall | C31×C71 ⋊ C22 |
| Sylow | C71 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×D71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C31×C71 | C22 |
| LCS | G ▷ C31×C71 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
629 conjugacy classes — view the full character table.
| maximal subgroup of | D71×D31⋊C3, C3×D31×D71, D71×D93, … |
| maximal normal subgroup of | D71×D31⋊C3, C3×D31×D71 |
| maximal quotient of | C3×D31×D71, D71×D93, D31×D213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8804, 6);